A two species non-autonomous competitive phytoplankton system with nonlinear inter-inhibition terms and one toxin producing phytoplankton is studied in this paper. Sufficient conditions which guarantee the extinction of a species and the global attractivity of the other one are obtained. Some parallel results corresponding to Yue (Adv. Differ. Equ. 2016Equ. :1, 2016Equ. , doi:10.1007 are established. Numeric simulations are carried out to show the feasibility of our results.

We consider a discrete competition model of plankton allelopathy with infinite deviating arguments of the form

A non-autonomous discrete Lotka-volterra commensal symbiosis model with Michaelis-Menten type harvesting is proposed and studied in this paper. Under some very simple and easily verified condition, we show that the system admits at least one positive periodic solution.

A Lotka–Volterra predator–prey system incorporating fear effect of the prey and the predator has other food resource is proposed and studied in this paper. It is shown that the trivial equilibrium and the predator free equilibrium are both unstable, and depending on some inequalities, the system may have a globally asymptotically stable prey free equilibrium or positive equilibrium. Our study shows the fear effect is one of the most important factors that lead to the extinction of the prey species. Such a finding is quite different from the known result. Numeric simulations are carried out to show the feasibility of the main results.

By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. Example together with its numerical simulation shows that the main results are verifiable.